Regulator of the ClocJc-iwrk of Equatoreals. 591 



cross-arm, carrying at the ends small weights. When the regulator 

 is made to revolve with a certain velocity, the centrifugal force of 

 the balls bends the springs till the balls just touch the inner surface 

 of a drum which surrounds the regulator : the smallest additional 

 velocity causes the balls to press against the drum and create a 

 friction which immediately reduces the velocity ; and the drum is 

 made slightly conical, so that by raising or depressing it the velocity 

 may be altered at pleasure. This construction not only partakes 

 of the defects common to all the others, but is liable besides to this 

 peculiar objection, that the determinate rate will depend most es- 

 sentially on the strength of the springs, and will therefore depend 

 on temperature and other varying causes. The other constructions 

 (which were practically introduced by Mr. Sheepshanks) depend 

 upon the same principle as that of the governor of the steam-en- 

 gine. Two balls suspended from the upper part of a vertical axis, 

 by rods of a certain length, are made to expand by the rotatory ve- 

 locity of the axis ; and this expansion, when it reaches a certain 

 extent, is made to press a lever against some revolving part, and 

 thereby to create a friction which immediately checks the velocity. 

 In some cases the balls are suspended bj^ rods from the extremities 

 of a horizontal arm carried by the vertical axis. This construction, 

 adopted in the south equatoreal of the Royal Observatory, may be 

 considered analogous to Fraunhofer's, substituting for the springs 

 the gravity of the balls; — a change which can hardly fail to be ad- 

 vantageous. 



Now, the uniformity of rotatory motion of the spindle, in these 

 various constructions, depends entirely on this assumption ; that if, 

 upon the whole, the retarding forces are equal to the accelerating 

 forces, the revolving balls will move in a circle and in no other 

 curve. But this assumption is not correct. If, for instance, we 

 consider the case of balls, suspended as in the governor of the 

 steam-engine; the motion of each of the balls maybe the same 

 (omitting the moments of inertia of the various parts of the machine, 

 which are trifling) as that of a ball, suspended by a string, and put 

 in motion by an arbitrary impulse ; and a ball so suspended may 

 move in a curve differing insensibly from an ellipse. Now this 

 elliptic motion actually takes place. In some instances observed 

 by the author, the balls of the regulator, instead of revolving in a 

 circle, revolved in an ellipse of considerable excentricity, and the 

 rotatory motion of the spindle was therefore exceedingly variable. 

 The effect of this irregularity on the motion of the equatoreal, 

 whether the inequalities of motion are followed by the polar axis, 

 or merely communicate a general tremor to the frame, must be 

 injurious. 



The inequality now mentioned is only one case of a very ex- 

 tensive theorem, which may be thus enunciated : — " Whenever tlie 

 equilibrium of forces requires that a free body be brought to a de- 

 terminate position, either absolute or relative to other parts of the 

 mechanism with which it may be connected, the body will not re- 

 main steadily in that position of equilibrium, but will oscillate on 



